It's not known what Vesser's crime was before he got sent to SAR TOP.
After taking on a human form, Vesser was sent by Zin to negotiate a deal with Nestov - in exchange for certain equipment by the next day, Nestov would be paid $10,000 - the first $5,000 been paid in advance. Nestov - first commenting on how Vesser's human form looked better then his 'usual' self - refused the money, cracking jokes all the time during his conversation, while asking questions about 'getting in' and helping Zin's operation. However, Vesser tells him that Zin already has 'the best' - referring to a female Desserian called Zareth, whom Nestov calls 'a legend'.
Continually asking questions, Vesser reveals only slight details - saying that Zin has 'taken an interest in art', with Nestov understanding that Zin wants Zareth to steal something art-related. However, Vesser's hypersensitive smell picks up on Nestov's pheromones - realizing he is lying. As he prepares to attack Nestov, Cole/Daggon appears. As Vesser tries to run, Cole throws Nestov on top of Vesser before using his hyperspeed to get in front of Vesser as he gets up and tries to continue running, Sure enough, Cole appears right in front of him before easily taking his life force.
Following this, Cole took the $5,000 that Vesser was offering to Nestov and - after giving Nestov a small portion - stated he and Mel would give the rest to charity (much to Nestov's annoyance).
Tracker (TV Series) - Episode 12: To Catch a Desserian